The scattering theory for the Klein Gordon equation, with time-dependent potential and in a non-static space-time, is considered. Using the Klein Gordon equation formulated in the Hubert spaceL2(R3) and the Einstein’s relativistic equation in the spaceL2(R3, dx) and establishing the equivalence of the vacuum states of their linearized forms in the Hubert spaceL2(R3) with the help of unique symmetric symplectic operator, the time evolution unitary operatorU(t) has been fixed for the Klein Gordon equation, incorporating either the positive or negative frequencies, in the infinite dimensional Hubert spaceL2(R3).
